Transcritical flow over obstacles and holes: forced Korteweg–de Vries framework

This paper extends a previous study of free-surface flow over two localised obstacles using the framework of the forced Korteweg–de Vries equation, to an analogous study of flow over two localised holes, or a combination of an obstacle and a hole. Importantly the terminology obstacle or hole can be reversed for a stratified fluid and refers more precisely to the relative polarity of the forcing and the solitary wave solution of the unforced Korteweg–de Vries equation. As in the previous study, our main concern is with the transcritical regime when the oncoming flow has a Froude number close to unity. In the transcritical regime at early times, undular bores are produced upstream and downstream of each forcing site. We then describe the interaction of these undular bores between the forcing sites, and the outcome at very large times.

Comparison between 2D Shallow-Water Simulations and Energy-Momentum Computations for Transcritical Flow Past Channel Contractions

Multidimensional simulators of channel and river flow are widely used in industry and academia, raising the question about whether the classical one-dimensional theory of open-channel flow remains relevant in hydraulic engineering. Channel contractions that induce transcritical flow are interesting scenarios to test the classical 1D theory against multidimensional simulations, because supercritical flow in channels of variable width leads to multidimensional flow structures. Transcritical flows are important in practice, because the ensuing hydraulic jumps and regions of supercritical flow may damage hydraulic structures that otherwise operate under tranquil conditions. We compare well-resolved simulations of the 2D shallow-water Equations (SWE) with 1D energy-momentum calculations for flow past symmetric channel contractions. We analyze the accuracy of the classical energy-momentum gradually-varied flow theory to predict the onset of regime transitions and the location of hydraulic jumps. We test the relative performance of the 1D theory for different constriction geometries, and identify the flow mechanisms behind the discrepancies between the 1D and 2D predictions. The grid resolution used in the 2D SWE plays an important role in these predictions, because coarse-grid 2D simulations yield essentially quasi-1D results. Considering its simplicity and negligible computational cost compared with the 2D SWE simulations, the classical 1D theory performs remarkably well for a wide range of flow conditions and contraction geometries. In contrast, we observe large deviations between the 1D and 2D models in flow past abrupt contractions with a large width ratio, as expected. Only modified versions of the 1D theory, taking into account intense local head losses and the propagation of spatial flow structures downstream from the contraction, can succeed at describing these flow scenarios.

Applicability of Preissmann box scheme for calculation of transcritical flow in pipes

The accurate computer simulation of pipe flow is of great importance in the design of urban drainage. The Preissmann box scheme is usually used to model a wide range of subcritical and supercritical flows. However, care must be taken over the modelling of transcritical flows since, unless the correct internal boundary conditions are imposed, the scheme becomes unstable. In this paper, using the scheme in conjunction with the reduced momentum equation and applying boundary condition structure inherent to subcritical flow to all regimes, is an approach that enables efficient numerical simulation of transcritical flows in pipe networks. The approach includes three steps. First, a unified mathematical model which is based on the Preissmann slot model is derived. Second, the Preissmann box scheme is used to solve the set of equations, by analyzing and discussing the origin of the invalidity of applying the scheme, and a numerical model suitable for transcritical flow is proposed by the method of changing the convection acceleration term. Third, the numerical model is assessed by comparison with analytical, experimental and numerical results. The proposed models verified that this method can make the Preissmann box scheme applicable to the computation of transcritical flow in pipes.